Organometallics 1995,14,63-69
63
A Theoretical Study of the (Cyc1obutane)diazadivanadium Complex Nazzareno Re and Antonio Sgamellotti Dipartimento di Chimica, Universiti? di Perugia, Via Elce di Sotto 8, I-06100Perugia, Italy
B.Joakim Persson and Bjom 0. ROOS* Department of Theoretical Chemistry, Chemical Centre, P.O. Box 124,S-22100 Lund, Sweden
Carlo Floriani Section de Chimie, Universitt! de Lausanne, Place du ChEiteau 3, CH-1005,Lausanne, Switzerland Received May 10,1994@
Ab initio CASSCFICASPTB calculations have been carried out on the V2NzHs complex, as a model of a series of (cyc1obutane)diazadivanadium complexes, in order to study the electronic structure and bonding in these complexes. Analogous calculations were performed also on the cationic and anionic species in order to study the behavior of the complexes toward oxidation and reduction. Geometry optimizations have been performed on the lowest singlet and triplet states and on the ground states of the ions, using wave functions of the restricted active space ( U S )SCF type. Dynamic correlation effects are included by means of second-order perturbation theory (CASPTB) with a CASSCF reference function based on a n active space comprising the V-V bonding and antibonding orbitals. The results indicate the presence of a weak cr metal-metal bond and a relatively large singlet-triplet splitting (8400 cm-l), with the singlet as the ground state. The computed structure for the singlet state is in agreement with experiment.
1. Introduction The synthesis of a series of novel binuclear complexes of V(W) with two bridging arylimido ligands has recently been rep0rted.l Complexes, of the type (L2VkN(p-MeC&)l}2 with L = CHzPh, Mes = 2,4,6-Me&Hz, hereafter called complex 1 and 2, respectively, show a short V-V distance in the range 2.45-2.50 A. Although rare, analogous compounds with heteroatom ligands on vanadium atoms have also been synthesized with similar V-V distance^.^-^ Such bond lengths fall in the typical range for single vanadium-vanadium bonds.'j Magnetic susceptibility measurements1 indicate diamagnetic character and therefore spin pairing of all the electrons. Both features suggest a single bond between the two V(W) dl species. However there are only few examples of metal-metal bonded divanadium complexes5 and they must be considered labile entities. Moreover, recent ab initio calculations on bridged dinuclear complexes of early-transition metals6-15 have shown an interesting interplay between the metalAbstract published in Advance ACS Abstracts, November 1,1994. (1)Solan, G.;Cozzi, P. G.; Floriani, C.; Chiesi-Villa, A,; Rizzoli, C. Organometallics 1994,13,2572. (2)Ruiz,J.; Vivanco, M.; Floriani, C.; Chiesi-Villa, A.; Rizzoli, C. J. Chem. Soc., Chem. Commun. 1991,214. (3)Ruiz, J.; Vivanco, M.; Floriani, C.; Chiesi-Villa, A.; Rizzoli, C. Organometallics 1993,12,1811. (4)Preuss, F.; Overhoff, G.; Becker, H.; Hausler, H. J.;Frank,W.; Reiss, G. 2.Anorg. Allg. Chem. 1993,619,1827. (5)Messerle, L. Chem. Rev. 1988,88, 1229. (6)Cotton, F. A.; Diebold, M. P.; Shim, I. Inorg. Chem. 1986,24, 1510. (7) h i f , A. M.; Cowley, A. H.; Pakulski, M.; Norman, N. C.; Orpen, A. G.Organometallics 1987,6,189. (8)Luthi, H. P.;Bauschlicher, C. W., Jr. J.Am. Chem. SOC.1987, 109,2046. @
0276-733319512314-0063$09.00/0
metal and the metal-ligand interactions. It is therefore of interest to study theoretically the electronic structure and the chemical bonding in such complexes. The real systems have two transition metals and large ligands, which would be prohibitively expensive for accurate ab initio calculations, especially when correlation energy is to be included and geometry optimization is to be performed. Two strategies are usually employed in such cases: either to deal with real systems performing low accuracy calculations or even using model hamiltonians (e.g. extended Huckel) or to perform highly accurate calculations on appropriate model systems. We have chosen the latter approach, taking the {H2V@-NH)}2 species, 3,as a model system of these complexes and performing accurate ab initio calculations. The chosen system is in our opinion a chemically significant model and represents well the V2N2 unit of the real complexes 1 and 2. The ab initio complete active space (CAS) SCF method and second-order perturbation theory correction (CASPT2)to the CASSCF wave function have been used with the molecular orbitals expanded in atomic contracted Gaussian-type functions. The CASSCF method is used to obtain a zeroth-order wave function where (9)Mougenot, P.; Demuynck, J.; Benard, M.; Bauschlicher, C. W., Jr. J.Am. Chem. SOC.1988,110,4503. (10)Weber, J.; Chermette, H. Organometallics 1989,8, 2544. (lUPoumbga, C.; Daniel, C.; Benard, M. Inorg. Chem. 1990,29, 2337. (12)Poumbga, C.; Daniel, C.; Benard, M. J.Am. Chem. Soc 1991, 113, 1090. (13)Rohmer, M.-M.; Benard, M. Organometallics 1991,10, 157. (14)Cotton, F. A.; Daniels, L. M.; Murillo, C. A. Inorg. Chem. 1993, 32,2881. (15)Rohmer, M.-M.; Benard, M. J.Am. Chem. SOC.1992,114,4785.
0 1995 American Chemical Society
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64 Organometallics, Vol. 14, No. 1, 1995
all spin couplings in the vanadium atoms 3d shell are properly treated and near degeneracy effects are taken into account. The CASPT2 correction to this CASSCF wave function is used to account for the dynamic correlation effects which are necessary in order to make reasonable quantitative predictions of the singlettriplet splitting energy. The CASPT2 method has recently been shown to yield accurate binding energies for the transition metal diatomics Ni2 and Cu2.16 As the complexes discussed here are reported to show an interesting redox reactivity,l analogous calculations have been performed also on the cationic and anionic species in order to study their behavior toward oxidation and reduction. 2. Computational Details
Generally contracted basis sets of the averaged atomic natural orbital (ANO)type have been used throughout this study. They have been obtained from (17s12p5d40, (14s9p4d30, and (8s4p3d) primitive sets for the vanadium, nitrogen, and hydrogen atoms, respectively. The ANO’s were constructed by averaging over several atomic states and positive and negative ions.17 They were contracted to W,6s4p3dlfl, [N,4s3p2dlfl, and [H,3slpl. The lowest states of singlet and triplet character were studied at essentially two levels of accuracy. The purpose was to compute the relative energies of the different spin states using multiconfigurational secondorder perturbation theory (CASPT2).18-20The CASpT2 calculation is based on a reference function of the complete active space (CAS) SCF type.21p22 Thus a CASSCF calculation has first t o be carried out. The choice of the active orbital space is crucial, since it is important that all near-degeneracy effects are included at the CASSCF level. If not, CASPT2 will not be a valid approach for treating remaining correlation effects. In a weakly bonded system like V2N2H6, it is not obvious which orbitals have to be included in the active space. Therefore the restricted active space (RAS) SCF methodB was used in the preliminary studies. This approach was also used for the geometry optimizations. In the CASSCF method,21s22the wave function is defined through the choice of the active orbital subspace and the number of active electrons. The wave function includes all the configuration state functions which can be generated by distributing the active electrons among the active orbitals in all possible ways. In the (H2V(p-NH)}2 molecule there are 26 valence electrons and 26 valence orbital which would lead, of course, to an active space much too big for a feasible CASSCF calculation. M e r some trial studies, we realized that, Chem. Phys., submitted. (17) Pierlott, K.: Dumez, B.: Widmark, P.-0.: Roos, B. 0. Medium size an0 basis sets’for the atoms H-Kr. To be published. (18)Andersson, K.; Malmqvist, P.-A.; Roos, B. 0.; Sadlej, A. J.; Wolinski, K. J. Phys. Chem. 1990,94, 5483. (lS)Andersson, K.;Malmqvist, P.-A.; Roos, B. 0. J . Chem. Phys. 1992,96, 1218. (20) Andersson, K. Multiconfigurational Perturbation Theory. Ph.D. thesis, University of Lund, Theor. Chemistry, Chem. Center, Lund, Sweden, 1992. (21) Roos, B. 0.;Taylor, P. R.; Siegbahn, P.E. M. Chem. Phys. 1980, 48, 157. (22)Roos, B. 0. Int. J . Quant. Chem. 1980,514, 175. (23) Malmqvist, P.-A.; Rendell, A.; Fbos, B. 0 .J . Phys. Chem. 1990, 94, 5477.
for a balanced description of the electronic structure in the metallacycle unit, the wave function should include terms necessary to describe at least the vanadiumvanadium, the vanadium-nitrogen, and the vanadiumhydrogen bonds. However, this leads to an active space of 22 orbitals with 22 electrons, which is still prohibitively big for a conventional CASSCF calculation. We therefore used a restricted active space ( U S )SCF scheme. This is a generalization of the CASSCF method in which, instead of a single active space, three active spaces are distinguished and called RAS-1, RAS-2 and RAS-3, respectively. Again, a certain number of electrons are distributed among the three orbital spaces, but now with the added restriction that at most a specified number of holes are allowed in the RAS-1 space and a t most a specified number of electrons are allowed in RAS-3. The present RASSCF wave function used 22 active orbitals corresponding to the V 3d, N 2p, and H(V) 1s orbitals. Two of these orbitals (the HOMO and the LUMO) were placed in the RAS-2 space; at most two holes were allowed in the RAS-1 space and a maximum of two electrons in RAS-3. This is equivalent to performing an MR-SDCI calculation with one (or two) reference configurations, in a small but optimized orbital space. The two reference configurations (one for the triplet state) are necessary to take into account the near degeneracy of the HOMO and LUMO orbitals, which leads to a high weight of the biexcited configuration. The RASSCF calculations showed that apart from the HOMO-LUMO pair, no severe near degeneracies occurred in the wave function. It was therefore decided that a CASSCF wave function with two active orbitals should be used as the reference function for the CASPT2 treatment. In the CASPT2 method, a Moller-Plesset-like secondorder perturbation theory is used, with the CASSCF wave function as the unperturbed wave function. The zero-order hamiltonian is built from a Fock-type oneelectron operator that reduces to the Moller-Plesset operator for a closed-shell case. The CASPT2 method computes the first-order wave function and the second order energy in the full space of configurations generated by the basis set. All calculations were performed in the “nondiagonal”approach, i.e. the full Fock matrix (including the nondiagonal elements) were used in the construction of the zero-order hamiltonian. For both the singlet and the triplet states the CASSCF calculation with two electrons in two active orbitals (the HOMO and LUMO) was followed by CASPT2 calculations differing only in the number of correlated electrons. In a first calculation all valence electrons, originating from the vanadium 3d, the nitrogen 2s, and 2p, and the hydrogen 1s orbitals, were correlated; in the second calculation also the vanadium core 3s and 3p orbitals were included. Recent studies of the electronic spectra of transition metal ions have shown that 3s,3p correlation effects can have a sizable effect on relative energ i e which ~ ~ ~is to a large extent determined by (3pI2 (3d)2 type excitations. Studies of hexacyanometalate complexes25showed that these core correlation effects are not specific to the free atoms, but also occur in
-
(24) Pierloot, K.; Tsokos,E.; Roos, B. 0. Chem. Phys. Lett. 1993, 214, 583.
(25) Pierloot, K.;Van Praet, E.; Vanquickenborne, L. G.; Fbos, B. 0. J . Phys. Chem. 1993,97, 12220.
A Theoretical Study of (Cyc1obutane)diazadivanadium
“tL
Organometallics, Vol. 14,No.1, 1995 65 Table 3. Natural Orbital Occupation Numbers for the Lowest Singlet and Triplet States of [Vfifi], Metal Character, and Metal Bonding Character of These Orbitals NO 9% 4b3, 5bzU lbi, 7b1, 3b3, loa, 8biU
Figure 1. The model system {H2V@-NH)}2 studied. Table 1. Optimized (RASSCF) Geometries for the [V2N&J Complex in the Lowest Singlet and Triplet States (units, angstroms and degrees) V-V V-N V-H N-H LHVH LA* 3Blu expl“
2.438 2.691 2.487
1.836 1.860 1.853
1.668 1.667
0.997 0.996
123.5 121.2
For the ((Mes)2V~-@-MeC&)])z complex.
Table 2. Calculated Triplet-Singlet Splittings, cm-’, at Different Levels of Theory
AEn (vertical) AEsr (adiabatic)
6500 4060
9550 7450
9860 8400
complexes. Their importance for the singlet-triplet splitting in the present system therefore cannot be neglected. Geometries have been optimized a t RASSCF level for both the lowest singlet and triplet states under a D2h symmetry constraint. The coordinate system has been chosen such that the z axis is in the V-V direction and the planar VzN2 unit lies in the yz plane (cf. Figure 1). All computations were performed with the MOLCAS-2 quantum chemistry package,26 implemented on IBM RS6000 workstations.
3. Results and Discussion The RASSCF geometry optimization of the complex 3 in the lowest singlet and triplet states leads to the optimized geometries reported in Table 1. The relative energies of the two electronic states are presented in Table 2. At all levels of theory, the ground state is a closed shell lAp state with the lowest triplet state, 3Blu, about 1 eV above. The dynamic correlation effects treated with the CASPT2 method leads to an increase in the energy separation. A slight further increase is obtained by including also the 3s,3p correlation effects. The optimized geometry for the singlet state of the model molecule is close to the experimental geometry for complex 2. This confirms the close analogy of the chosen model to the real molecule. The optimized (26)Andersson, K.;Blomberg, M. R. A.; Fiilscher, M. P.; Kello, V.; Lindh, R.; Malmqvist, P.-A.; Noga, J.; Olsen, J.;RQOS,B. 0.; Sadlej, A. J.; Siegbahn, P. E. M.; Urban, M.; Widmark, P.-0. MOLCAS Version 2 User’s Guide. Dept. of Theor. Chem., Chem. Center, Univ. of Lund, Lund, 1992.
singlet occno.
metal%
triplet mcno.
metal%
1.97 1.96 1.98 1.95 1.97 1.97 1.69 0.31
8 22 18 19 27 19 99 91
1.98 1.97 1.97 1.96 1.97 1.98 1.00 0.99
9 25 19 20 28 21 98 98
character
6
n n 6 6*
n* U
a*
geometry for the triplet state is, instead, very different, with a much longer V-V distance. An analysis of the electronic structure of the singlet ground state may be obtained from the RASSCF calculations. The leading configuration in the final RASSCF expansion corresponds to (3daI2,which has a weight of 73%. The second most important configuration corresponds to a (3du12 (3da*12electron excitation with a weight of 12%,while all other configurations account for less than 0.5% each. The results of the RASSCF calculation can also be interpreted in terms of population of bondinglantibonding pairs of natural orbitals (NOS) with some metal character. Table 3 gives the natural orbital occupations of these NOS for both the singlet and the triplet states. It is clear from these results that there is only one pair of orbitals with the dominating metal character, (10a&3blU), corresponding to the vanadium u and 8 orbitals. A more detailed analysis of these two natural orbitals reveals that loa, has a metal-metal bonding character and is essentially built from overlapping hybrid 3d orbitals (about 89% d,z and 11%dXz-,,z),while 8b1, is the corresponding antibonding orbital. Moreover the occupation analysis gives for the singlet state a u1.69a*0.31 configuration, which is characteristic of a relatively strong metal-metal bond. We recall12that the relative distribution of the population between the bondinglantibonding pair of NOS determines the degree of delocalization of the corresponding electron pair. That is, an almost zero population of the antibonding NO indicates an almost complete delocalization of the electron pair and therefore a strong metal-metal bond, while nearly equal populations for the two NO indicates an almost complete localization of the two electrons, one on each metal atom, and antiferromagnetic coupling between them. This metal-metal bonding picture is consistent with the computed relatively large singlettriplet energy splitting, which at the most accurate CASPT2 level is 9860 cm-’, in agreement with the diamagnetic character observed for such complexes. Although the formal V-V bond order in this V(rV)-V(rV) complex is 1,the partial occupation of the a* NO leads to an actual lower bond order. Indeed, the bond order computed from the RASSCF wave function as
-
where ~(Vzi) represents the contribution of the occupation of orbital i, which can be assigned to the dimetallic unit on the basis of the metal character of that orbital, is 0.7 and clearly shows the partial localization effects. The electron density generated by this ala* NO pair is represented in Figure 2. It shows the mainly dzz
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66 Organometallics, Vol. 14, No. 1, 1995
Table 4. Atomic Charges and Partial Mulliken Gross Atomic Populations for the Lowest Singlet and Triplet States of [VzNfi] Complex and for the HzV2+ Fragment in Its *AI Ground State
0
V charge 4s 4P 3dz1 3ds-9 3dxY 3dxz 342 3d H(V) charge NH charge
Figure 2. Plot of the summed electron density from the V-V bonding and antibonding orbital pair. The values of the density contours are f0.30, k0.25, f0.20, f0.15, fO.lO, k0.04, f0.02, f O . O 1 , f0.005, k0.0025, and f0.00125 e/au3.
n
W
5bzu
3b3g
4b3"
Figure 3. The six molecular orbitals involved in the bonding of the vanadium atoms to the ligands. character of the d hybrids, which constitute such bondcomponent. indantibonding pair, with a minor 3d,~--~z As Table 3 illustrates there are also six lower lying frontier orbitals with a relevant metal character, namely gag, 4b3,, 5bzu, 1blg, 7bh, and 3ba, showing an almost negligible degree of localization (with occupations in the range 1.96-1.98). These six bonding orbitals represent essentially the four combinations of the 2py and 2pz orbitals of the bridging nitrogen atoms with the unoccupied metal-metal orbitals of appropriate symmetry in the metallacycle plane bz),and the analogous two combinations of the 2px nitrogen orbitals with corresponding 3d metal orbitals (cf. Figure 3). The corresponding electron pairs take part in delocalized metal-bridging ligand interactions giving rise to the four vanadium-nitrogen u bonds and two delocalized n bonds of the metallacycle moiety. "he x or 6 metalmetal bonding character Qf four of these orbitals overcomes the antibonding character of the remaining two (see Table 3) and indicates an appreciable net contribution to the V-V bond order (about 0.2 of mainly n character). Thus, the overall metal-metal interaction results from the interplay of the direct vanadiumvanadium bond and through the vanadium-ligand bonds. This bonding picture for the metallacycle moiety is in agreement with intuitive considerations based on the ionic and covalent models that are commonly used
singlet
triplet
fragment
1.05 0.50 0.32 0.93 0.73 0.25 0.78 0.38 3.07 -0.20 -0.66
1.10 0.51 0.33 0.99 0.64 0.22 0.72 0.42 3.00 -0.20 -0.69
1.84 0.35 0.18 0.96 0.50 0.00 1.17 0.00 2.63 +0.08
in connection with electron counting. Indeed, the imino ligands must be formally considered as ( H N Y while the metal is V(IV). Each vanadium ion (with a dl configuration)accepts one electron pair from each of the NH ligands, forming two V-N u bonds, and one n electron pair from one of the NH ligands, forming a delocalized V-N n bond of order 0.5 with the two imino ligands. The d electrons on the two vanadium atoms couple together to form a u metal-metal bond. This picture is confirmed by the Mulliken population analysis of the RASSCF wave function reported in Table 4. The Mulliken gross atomic charge on each metal atom is 1.05, which is of course much lower than the formal 4 value because of the covalent bonding with the bridging NH and the hydrogen ligands. An analysis of the interactions within the metallacycle moiety can be performed by comparing the Mulliken analysis population of our complex with that of the monomeric HzV+ fragment, also reported in Table 4. For these fragments, still of V(IV) character, the positive net charge is 1.84. The metallacycle formation thus leads to a reduction of the vanadium charge by 0.79 units. Most of this extra electronic charge is distributed on the metal 3dXZy2, 3d,, 3d,, and 3dyz orbitals and is due to the bonding interactions of these formally unoccupied 3d orbitals with the NH bridging ligands within the metallacycle unit as described above. Among the results of our calculations, we see from Table 4 that the loa, NO representing the V-V u interaction is an almost pure (99%) metallic orbital. Although unusual in SCF or semiempirical calculations, in which a relevant contribution from the NH u lone pair is expected (see, for example, ref 27), a HOMO of almost pure metallic character describing a metal-metal bond may be quite common in accurate calculations including electron correlation.11-l3 The electronic structure of the triplet state, 3Blu,is described by a configuration (cf. Table 3) corresponding to a nonbonding character of the metalmetal interaction. However, the nature of the metalbridging ligand interactions in this triplet state is essentially identical t o that found for the singlet state and described above. This is further illustrated by the NO occupation numbers and the Mulliken analysis presented in Tables 3 and 4. The character of the bond is reflected in the optimized geometry found for the triplet state where the metal-metal distance is elongated to 2.69 A (typical of nonbonded V-V interactions). (27) Shaik, S.; H O E " , R.; Fisel, C. R.; Summenrille, R. H. J . Am. Chem. SOC.1980,102,4555.
A Theoretical Study of (Cyc1obutane)diazadivanadium
Organometallics, Vol. 14, No. 1, 1995 67
Table 5. Optimized Geometries for the Dication, Monocation, Monoanion, and Dianion Species in Their lA,, 2Ag,2Blu,and 'A, Ground States (units, angstroms and degrees)
Table 8. Atomic Charges and Partial Mulliken Population Analysis for the Dication, Monocation, Monoanion, and Dianion Species in Their lA,, 2A,, 2Blu,and 'A, Ground States
dication monocation monoanion dianion
V-V
V-N
V-H
N-H
2.688 2.549 2.537 2.625
1.811 1.816 1.870 1.922
1.585 1.626 1.759 1.836
1.015 1.003 1.007 1.OOO
LHVH
123.9 125.0 116.5 104.4
Table 6. Relative RASSCF and CASPTZ (both with and without 3s,3p correlation) Energies (in kcal/mol) for the Dication, Monocation, Monoanion and Dianion Species in Their lAg, zA,, 2Blu,and IAg Ground States, with Respect to the Ground State of the Neutral Compound RASSCF
CASF"2
CASPT2 (3s3p)
488 184 -28 63
512 150 -30 122
502 142 -29 120
dication monocation monoanion dianion
Table 7. Natural Orbital Occupation Numbers for the Dication, Monocation, Monoanion, and Dianion Species in Their lAg, 2A,, %lU, and 'A, Ground States NO
dicat
monocat
monoan
dian
1.98 1.96 1.98 1.95 1.97 1.97 0.02 0.01
1.95 1.97 1.96 1.98 1.97 1.98 0.96 0.09
1.96 1.98 1.97 1.98 1.97 1.96 1.91 1.03
1.96 1.98 1.97 1.98 1.98 1.96 1.98 1.97
The structure is, however, still kept together by the strong metal-bridging ligand interaction. The vertical singlet-triplet energy separation computed a t the most accurate CASPT2 level is 9860 cm-l (cf. Table 2). The large values found for this splitting rules out any possible thermal contamination of the singlet ground state and is therefore in agreement with the diamagnetic character found experimentally for the complexes 1 and 2. From Table 2 we see also that geometry relaxation leads to a slightly lower value of the adiabatic singlet-triplet splitting, 8400 cm-l. It is moreover worth noting that the energy splitting depends on the inclusion of dynamic correlation. The RASSCF calculation underestimates the splitting, which is probably due t o the inadequate accounting for the differential Pauli correlation effects in the RASSCF wave function. We have performed RASSCF and CASSCF/CASPT2 calculations-also on the mono- and dianion and on the mono- and dication species, {H2Vb-NHl}22+,4, (H2Vb-NHIh+, 5, {H2Q-NH1>2-, 6, and {H2VCu-NH1h2-, 7, in order to study the behavior of complex 3 toward reduction and oxidation. The corresponding optimized geometries and relative energies are reported in Tables 5 and 6. In Table 7 we report the natural orbital occupation numbers of the NOS with some metal character for all four charged species. A detailed analysis of the orbitals shows that they are qualitatively similar to those of the neutral species 3,describing the a and n vanadium bridging ligands interactions and discussed above. However, all these orbitals have a higher metallic character in the cationic species and a lower metallic character in the anionic species. Moreover, from Table 7 we note that the configurations for these four charged species are approximatively (3da)O(3da*)O, (3d0)~(3da*)~, (3da)2(3da*)1,and (3dd2(3d8I2,
V charge 4s 4P 3dzr 3d~-~z 3 4 3du 3dYZ 3d H(V) charge NH charge
dicat
monocat
monoan
dim
1.32 0.43 0.28 0.11 0.86 0.25 1.07 0.72 3.01 0.09 -0.50
1.14 0.51 0.31 0.45 0.86 0.25 0.93 0.50 3.00 -0.04 -0.55
1.11 0.48 0.31 1.40 0.57 0.23 0.58 0.26 3.04 -0.39 -0.82
1.18 0.40 0.28 1.86 0.41 0.17 0.42 0.23 3.09 -0.58 - 1.02
respectively, going from the dication to the dianion, which formally corresponds to no metal-metal bond for the dication and the dianion species ...to a weak metalmetal bond (with a bond order of about 0.5) for the monocation and the monoanion. The different V-V bond strengths resulting from these electronic structures are reflected by the optimized geometries (cf. Table 5), with a metal-metal distance of 2.60-2.70 A for the dication and dianion species, similar to that found for the triplet state of the neutral species and t ical of nonbonded V-V interactions, and of 2.50-2.55 for the monocation and monoanion species, intermediate between those of the singlet and triplet states of the neutral molecule. The Mulliken analysis population for all these four charged species is given in Table 8. The main interesting feature in these results is the small change of the charge on the vanadium atom in going from the dication to the dianion. This redistrubution of the electron charge removed from or put into metallic 3da or 3 d 8 orbitals can be ascribed to the change in the metallic character of all the low lying frontier orbitals going from the neutral species to the cationic and anionic species, as reported above. A large fraction of the extra charge is located at the four hydrogens directly bound to the metal. Although this effect could be partly due to the extended basis set with many polarization functions, it is significant and should be even larger in the real system where hydrogens are substituted by the more polarizable mesityl groups. The hydrogen atoms (mesityl groups in the real system) act as effective reservoirs for the electrons put on the HOMO and LUMO orbitals. The analysis of the six low lying frontier orbitals representing the a and n vanadium-bridging ligand interactions for ionic species 4-7 shows that metalbridging ligand bonding is not overly weakened by oxidation or reduction. Moreover, the obtained V-N bond distances, although slightly elongated with respect to the neutral molecule in the anionic species, still fall in the range of typical vanadium-nitrogen bonds for all the four ionic species. This suggests that, in spite of the two lost or gained electrons, the metallacycle V2N2 unit is still a fairly strongly bound moiety so that complex 3 should survive both one or two electron oxidation or reduction steps. Considering the energy needed to form the four ionic species from complex 3 (cf. Table 6), it is found that mono- and dioxidation requires much energy (142 and 501 kcaymol, respectively) while mono and direduction are much easier with the first electron affinity positive; that is, the monoanion
T
68 Organometallics, Vol. 14, No. 1, 1995
Re et al.
Figure 4. Plots of the total density difference between the ionic species and the singlet ground state of the molecule. The figures show the density shifts in the V" plane with the vanadium atoms along a horizontal axis. Full contours correspond to an increased density and dashed contours to a decreased. The values of the density contours are f0.032, f0.016,f0.008, f0.004,f0.002, fO.OO1, f0.0005,and f0.00025 e/au3. is lower in energy than the neutral complex (by 29 kcaV mol). Also the computed energy required for the double reduction of the model {H2Vb-NHl}2 complex is only 120 kcaVmol and will be even lower considering that the real system has six mesityl groups instead of hydrogens which, because of their electron withdrawing properties, should further stabilize the dianion species. Moreover, taking into account solvation effects in the real liquid phase reactions, the results above suggest that monoreduction of complex 3 in solution should be easy and that also its direduction could be possible. The value for the second electron affinity is in a way artificial, since it has been computed to be negative. However, the extra electron naturally goes into a 3d antibonding orbital, which then becomes a closed shell. The calculation therefore describes the situation which would occur in solution, where the dianion is stable and the computed energy is more a measure of the solvation energy needed to make the ion stable. There is a strong negative correlation contribution to the relative energy of the dianion. The CASSCF value is only 63 kcaVmo1, which is almost doubled at the CASPT2 level of theory. This is somewhat surprising, since dynamic correlation is normally more important in the negative ions than in the corresponding neutral species.
The electron density difference for the four ionic species is shown in Figure 4. It is clear that ionization leads to a decreased density in the V-V bonding region, which is to some extent compensated by an increased density in the V-N and V-H regions. As a result, the corresponding bond distances decreases (cf. Tables 1 and 5). In the anions the extra electron goes into the antibonding V-V orbital, so even if the figure shows an increased density in this region the bond distance will increase. The decreased density in the V-N and V-H regions leads to elongated bonds. The results obtained for the mono- and dianionic species indicate that the 8b1, LUMO can be seen as a low-energy orbital available for the molecule to easily accept one or two electrons without undergoing drastic structure i alterations, the extra charge being buffered into the hydrogen atoms (mesityl groups). 4. Conclusions
The electronic structure and geometry of the model compound {H2VTp-NHl}2 in its lowest singlet and triplet state has been determined using multiconfigurational SCF methods with dynamic correlation effects on the total energy obtained using second-order perturbation
Organometallics, Vol. 14, No. 1, 1995 69
A Theoretical Study of (Cyc1obutane)diazadivanadium
theory. The molecule has been found to have a singlet ground state with the lowest triplet state about 1 eV higher in energy. The computed equilibrium geometry is in agreement with measured data for related compounds. Analysis of the wave function shows that the two vanadium atoms are bound together with a single bond in the singlet state, while no such bond exists in the triplet state. Corresponding calculations on the positive and negative ions yields structures with half a bond for the singly ionized systems and no V-V bond
for the doubly ionized systems. The first electron afinity is found to be positive.
Acknowledgment. The present work has been carried out within the program “Progetto finalizzato CNR Materiali Speciali per Tecnologie Avanzate”. Support by the Fond Nationale Suisse de la Recherche Scientifique and the Swedish Natural Science Research Council (NFR) is gratefully acknowledged. OM9403582
